Co-continuous microstructures through spinodal decomposition in ternary systems: A phase field study

Abstract

We have studied spinodal decomposition which leads to a three-phase microstructure in ternary alloys using computer simulations based on the ternary Cahn-Hilliard equations. All the alloys we have studied are in the same ternary phase diagram in which each of its constituent binaries is a regular solution, with all the regular solution constants being the same. In particular, we have focused our research on the ability of ternary systems to produce tricontinuous microstructures, by undertaking a systematic study of microstructure formation in in systems as a function of phase fractions (i.e., alloy composition), relative energies of the three interfaces, and relative mobilities of the three species. Spinodal decomposition in the most symmetric alloy in the most symmetric system (in which the three interfacial energies are equal, and the three species mobilities are equal) takes place through a simultaneous separation of each of the three species with equal ease. Thus, it leads naturally to a tricontinuous microstructure, just as SD in an equimolar binary alloy produces a bicontinuous microstructure. Such tricontinuous microstructures are also produced in this alloy under a variety of conditions employed in our study; they are also produced in alloys if their compositions are close to being equimolar. In off-symmetric alloys or in symmetric alloys under off-symmetric conditions in interfacial energies and / or species mobilities, the formation of microstructure may be rationalized using a framework of a two-stage sequence of decomposition. We have identified two such sequences: in one, the first stage produces regions which are richer and poorer in one of the species (say, C), and the second stage involves separation of species A and B within the formerly C-poor regions. In the other sequence, the first stage involves separation of the alloy to produce A-rich and Brich regions, followed by the second stage in which species C separates to the interfaces between the A-rich and B-rich regions. This framework has been used to analyze the microstructures produced in alloys with far from equimolar compositions (such as (c_A, c_B,c_C) = (25,25,50) and (40,40,20)). In such alloys, the volume fraction of the minority phase(s) is/are much smaller than that of the majority phase(s); this disadvantage causes them to form thin regions which are prone to breaking up. However, our framework allows us to identify a suitable combination of conditions (involving the interfacial energy and species mobilities) for which tricontinuous microstructures may still be obtained in these alloys. Essentially, under these optimal conditions, the first stage proceeds for a longer period, so that its products (the phase-separated regions) are thicker; when the second stage starts, phase separation in these thicker regions (or at the interface between these thicker regions) produces phase(s) which has/have a greater probability of being co-continuous. With these strategies (which arise from the framework of microstructure formation developed in this stydy), we show that it is possible to produce tricontinuous microstructures in alloys in which the volume fraction of one or two phases is as low as 0.25